Anatomy of Fermionic Entanglement and Criticality in Kitaev Spin Liquids

TL;DR

This paper investigates how non-trivial band topology influences entanglement entropy in Kitaev's honeycomb model, revealing universal contributions from edge states and classifying critical phases within known universality classes.

Contribution

It analytically links topological edge states to entanglement entropy and classifies critical phases in Kitaev spin liquids, extending understanding to generic topological insulators and superconductors.

Findings

Edge states contribute to entanglement entropy in gapped phases

Critical phases fall into Ising or XY universality classes

Universal lower bounds for entanglement entropy are established

Abstract

We analyse in detail the effect of non-trivial band topology on the area law behaviour of the entanglement entropy in Kitaev's honeycomb model. By mapping the translationally invariant 2D spin model into 1D fermionic subsystems, we identify those subsystems responsible for universal entanglement contributions in the gapped phases and those responsible for critical entanglement scaling in the gapless phases. For the gapped phases we analytically show how the topological edge states contribute to the entanglement entropy and provide a universal lower bound for it. For the gapless semi-metallic phases and topological phase transitions the identification of the critical subsystems shows that they fall always into the Ising or the XY universality classes. As our study concerns the fermionic degrees of freedom in the honeycomb model, qualitatively similar results are expected to apply also to generic topological insulators and superconductors.